reduced.h

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/** @file reduced.h
 */
/**
# Reduced gravity 
 
We re-express gravity in [two-phase flows](two-phase.h) as an
[interfacial force](iforce.h) as
\f[
-\nabla p + \rho\mathbf{g} = 
-\nabla p' - [\rho]\mathbf{g}\cdot\mathbf{x}\mathbf{n}\delta_s
\f]
with \f$p'= p - \rho\mathbf{g}\cdot\mathbf{x}\f$ the dynamic pressure and
\f$\rho\mathbf{g}\cdot\mathbf{x}\f$ the hydrostatic pressure. The corresponding 
potential is
\f[
\phi = [\rho]\mathbf{G}\cdot(\mathbf{x} - \mathbf{Z})
\f]
with \f$\mathbf{G}\f$ the gravity vector and \f$\mathbf{Z}\f$ an optional
reference level. */
 
coord G = {0.,0.,0.}, Z = {0.,0.,0.};
 
/**
We need the interfacial force module as well as some
functions to compute the position of the interface. */
 
#include "iforce.h"
#include "curvature.h"
 
/**
We overload the acceleration() event to add the contribution of
gravity to the interfacial potential \f$\phi\f$.
 
If \f$\phi\f$ is already allocated, we add the contribution of gravity,
otherwise we allocate a new field and set it to the contribution of
gravity. */
  
/** @brief Event: acceleration (i++) */
void event_acceleration (void) 
{
  scalar phi = f.phi;
  coord G1;
  for (int _d = 0; _d < dimension; _d++)
    G1.x = (rho2 - rho1)*G.x;
  
  if (phi.i)
    position (f, phi, G1, Z, add = true);
  else {
    phi = {0} /* new scalar */;
    position (f, phi, G1, Z, add = false);
    f.phi = phi;
  }
}